Shape-directed rotation of homogeneous micromotors via catalytic self-electrophoresis

Abstract

The pursuit of chemically-powered colloidal machines requires individual components that perform different motions within a common environment. Such motions can be tailored by controlling the shape and/or composition of catalytic microparticles; however, the ability to design particle motions remains limited by incomplete understanding of the relevant propulsion mechanism(s). Here, we demonstrate that platinum microparticles move spontaneously in solutions of hydrogen peroxide and that their motions can be rationally designed by controlling particle shape. Nanofabricated particles with n-fold rotational symmetry rotate steadily with speed and direction specified by the type and extent of shape asymmetry. The observed relationships between particle shape and motion provide evidence for a self-electrophoretic propulsion mechanism, whereby anodic oxidation and cathodic reduction occur at different rates at different locations on the particle surface. We develop a mathematical model that explains how particle shape impacts the relevant electrocatalytic reactions and the resulting electrokinetic flows that drive particle motion.

Fig. 1

Shape-directed particle rotation. a Schematic illustration of two platinum disks (a = 5.77 μm, δ = 100 nm) of opposite handedness rotating above a glass substrate in a solution of hydrogen peroxide. b The parametric particle shape depends on the number of fins n and the fin asymmetry c. c Optical microscope image of particles with n = 3 and c = 2 rotating clockwise at a speed of Ω = 1.5 ± 0.2 rad s⁻¹ in a 10 wt% solution of hydrogen peroxide (see Supplementary Movie 1). d Optical microscope image of multiple types of particles rotating in different directions and at different rates in a common environment of 10 wt% hydrogen peroxide (see Supplementary Movie 2). Scale bars are 20 μm

Fig. 2

Effect of shape asymmetry. The angular velocity Ω decreases with increasing shape asymmetry c for particles with different numbers of fins n. The inset shows the dependence on n for a constant asymmetry of c = 2. All experiments were performed in 10 wt% hydrogen peroxide. Error bars denote 95% confidence intervals for the mean velocity based on the analysis of at least 10 particles (see Methods). Dashed lines are only to guide the eye

Fig. 3

Experiments supporting a self-electrophoretic propulsion mechanism. a Angular velocity as a function of hydrogen peroxide concentration for particles with shape asymmetry c = 2 and different numbers of fins n. Error bars represent 95% confidence intervals for the mean velocity. b Angular velocity as a function of salt concentration for particles with n = 3 fins and shape asymmetry c = 2 rotating in 10 wt% H₂O₂. The inset shows the rotation reversal with addition of 0.33 mM of the cationic surfactant CTAB (see Supplementary Movie 3); scale bar is 20 μm

Fig. 4

Results of the self-electrophoretic propulsion model. a Kinetic mechanism for the electrocatalytic decomposition of H₂O₂ over platinum. b Computed ion concentrations C_i (left) and fluxes j_i (right) as a function of distance x from a planar Pt surface. Concentration is scaled by the bulk concentration $C_{\pm }^{\infty }={\left(K_{\mathrm{p}}{C}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}^{\mathrm{0}}\right)}^{1∕2}$, distance by the reaction-diffusion length $\lambda ={\left(D_{\pm }∕k_{-\mathrm{p}}{C}_{\pm }^{\infty }\right)}^{1∕2}$, and flux by the $j_{\pm }^{\infty }=D_{\pm }{C}_{\pm }^{\infty }\mathrm{∕}\lambda$. c Computed current density i (left) and fluid velocity u (right) around a circular Pt disk of radius a = 41λ and thickness δ = 0.72λ centered at the origin. The insets show magnified views of the current and flow near the edge of the disk. The maximum flow velocity is $u_{\max }=0.0082C_{\pm }^{\infty }{k}_{\mathrm{B}}T\lambda \mathrm{∕}\eta$, which corresponds to 8.6 μm s⁻¹ for the experimental conditions. d Computed angular velocity Ω as a function of the asymmetry parameter c for spinners with n = 2–6 fins and b = 0.3. Velocities are scaled by ${\mathrm{\Omega }}_{\mathrm{0}}=C_{\pm }^{\infty }{k}_{\mathrm{B}}Th\mathrm{∕}\eta a$, which is estimated to be 240 s⁻¹ for the experimental conditions. The inset shows the conformal mapping from disk to twisted star used in the calculation